The Phase Problem of X‐Ray Crystallography

With the invention some 200 years ago of the goniometer, an instrument for measuring the angles between the faces of a crystal, the science of crystallography was born. The goniometer made possible the discovery of the fundamental laws of descriptive crystallography: that the angles between the facial planes are determined by the chemical composition of the crystal and that the relative orientations of the facial planes follow a simple rule, the law of rational positions.

For almost 40 years physicists thought it impossible, even in principle, to determine complex crystal structures directly from the intensities of diffracted x rays.